Transitions between Turbulent States in Rotating Rayleigh-Bénard Convection

Weakly rotating turbulent Rayleigh-Bénard convection was studied experimentally and numerically. With increasing rotation and large enough Rayleigh number a supercritical bifurcation from a turbulent state with nearly rotation-independent heat transport to another with enhanced heat transfer is observed at a critical inverse Rossby number $1/{\mathrm{Ro}}_c\simeq 0.4$. The strength of the large-scale convection roll is either enhanced or essentially unmodified depending on parameters for $1/\mathrm{Ro}<1/{\mathrm{Ro}}_c$, but the strength increasingly diminishes beyond $1/{\mathrm{Ro}}_c$ where it competes with Ekman vortices that cause vertical fluid transport and thus heat-transfer enhancement.

Figure 1

The ratio $\mathrm{Nu}(\Omega )/\mathrm{Nu}(\Omega =0)$ as a function of $1/\mathrm{Ro}$ for $\mathrm{Ra}=4\times {10}^7$ and $\mathrm{Pr}=6.26$. Open black squares indicate the numerical results. The numerical error is approximately 0.2%, which is indicated by the size of the symbols. Inset: The thickness of the kinematic top and bottom BLs based on the maximum rms azimuthal [upper symbols: black circles (red squares) for top (bottom) BL] and radial [lower symbols: green diamonds (blue squares) for top (bottom) BL] velocities. The vertical dashed lines in both graphs represent $1/{\mathrm{Ro}}_c$ and indicate the transition in boundary-layer character from Prandtl-Blasius (left) to Ekman (right) behavior.

Figure 2

$\mathrm{Nu}(\Omega )/\mathrm{Nu}(\Omega =0)$ for $\mathrm{Ra}=2.73\times {10}^8$ and $\mathrm{Pr}=6.26$. Red solid circles: experimental data ($T_m=24°\mathrm{C}$ and $\Delta =1.00\mathrm{K}$). Open black squares: numerical results. The experimental error coincides approximately with the symbol size, and the numerical error is approximately 0.5%. Inset: Thickness of the kinetic BL. For dashed vertical lines and inset, see Fig. 1.

Figure 3

The normalized averaged rms vertical velocities $w_{\mathrm{rms}}$ for $\mathrm{Ra}=4\times {10}^7$ (left) and $\mathrm{Ra}=2.73\times {10}^8$ (right) as a function of $1/\mathrm{Ro}$. The black line (with asterisks) indicates the normalized volume-averaged value of $w_{\mathrm{rms}}$. The red line (with squares) and blue line (with diamonds) indicate the normalized horizontally averaged $w_{\mathrm{rms}}$ at the edge of the thermal BL based on the slope at, respectively, the lower and upper plate. The vertical dashed lines again indicate the position of $1/{\mathrm{Ro}}_c$.

Figure 4

Results for $\mathrm{Ra}=9.0\times {10}^9$ and $\mathrm{Pr}=4.38$ ($T_m=40.00°\mathrm{C}$, $\Delta =16.00\mathrm{K}$). (a) $\mathrm{Nu}(\Omega )/\mathrm{Nu}(\Omega =0)$ vs $1/\mathrm{Ro}$. The error bar is smaller than the size of the symbols. (b) Solid symbols: time-averaged LSC amplitudes $⟨{\delta }_0⟩/\Delta$ ($z=0$, circles) and $⟨{\delta }_t⟩/\Delta$ ($z=L/4$, squares) as a function of $1/\mathrm{Ro}$. Open symbols: rms fluctuations about the cosine fit [Eq. (1)] to the temperature data. (c) Vertical temperature variation $\Delta T_w/\Delta$ along the sidewall. (d) Circles: time-averaged normalized sidewall-temperature profile $⟨[T(\theta )-T_w]/{\delta }_0⟩$ at the horizontal midplane for $1/\mathrm{Ro}=1$ determined as in 15. Solid line: $\cos (\Theta -{\Theta }_0)$.